Introduction to Datums
James R. Clynch
February 2006
I.
What Are Datums – in Geodesy and Mapping?
A datum is the traditional answer to the practical problem of making an accurate map. If
you do not have a very accurate location on a benchmark in your area, you make a map
by choosing a mark and defining it as the reference point. You then survey outward and
make a map. It may not match other’s maps from adjacent areas at high accuracy
because you are on a different datum, the one you created.
If you wish to determine the relative location of a pair of points a few meters apart, the
solution is obvious. Just measure the difference with a tape measure. The issue of
orientation still exists though, but this can be solved using two "known" points to
measure a third. Or observations of the stars can be used to define north.
In effect this defines a local datum. The known point, together with some method for
determining the direction of north, define the location of points measured from it. If the
reference point is in error by 100 m north, so will all the points using this reference mark.
They move together. This of course assumes these errors are small, at least as compared
to the radius of the earth.
If you look at the legend of a topographic map, you will find that it lists the "datum" that
is used. In fact there may be several datums, one for horizontal, one for vertical etc.
These are important because they define the reference system that is used for the
coordinates.
Why is this important. Will if you use a navigation system (like GPS) that is not set to
the map datum, you can be off by 100m (usually) to a kilometer (sometimes). GPS
receivers are inherently on the WGS84 datum, but can be set to display locations in
several other datums.
A datum can be defined by specifying the ellipsoid, the coordinates of a single point and
the direction north. The point ties down the ellipsoid to the physical earth and also
implicitly defines the placement of the center of the earth. This location is called the
primary reference point. For North America, it is in central Kansas at a place called
Meade'
s Ranch.
The practical way to define a datum is with a whole set of reference markers and their
associated coordinates. They should be carefully surveyed together. This gives a network
that serves as a "realization" of the datum. This provides a practical set of points spread
out over the region covered. Surveyors use the closest survey marker that meets the
accuracy needs . You don'
t have to start all surveys in North America in Kansas.
1
This means that datums are the reference frames used in the construction of maps.
Things are complicated in practice as the same area may have two datums giving each
point two different coordinates. In addition datums were often generated by individual
countries, and did not match at the boundaries.
While there are about 20 common ellipsoids, most ellipsoids are used in multiple datums.
For example the number of datums on some popular ellipsoids are:
Ellipsoid
Airy 1830
Bessel 1841
Clarke 1866
Clarke 1880
International 1924
Number of Common Datums
2
7
9
26
47
This understates the true complexity and confusion. For example the North American
Datum of 1927 (NAD 27) is listed once for Clarke 1866 in the above table. But NAD 27
is really about 25 different datums. They are all on the Clarke 1866 ellipsoid, but have
different primary reference points. The continental NAD 27 is different than that in the
Bahamas or the one in Greenland or the one in Cuba ... This issue has not gone away with
the newer NAD of 1983. There are different datums called NAD 83 in different areas.
The uses of different ellipsoids arises from the variations in the shape of the true earth
and the difficulty of estimating the ellipsoid shape from a “limited” portion of the world,
such as Europe of North America. The scientist in each region took the data they had
and fit it to an ellipsoid.
This often resulted in different ellipsoid parameters (axis lengths) and center location.
The above figure exaggerates the differences between the European datum ellipsoid and
2
that for North America, but is essentially correct. Often the origin shift is the largest
difference in datum ellipsoids. This does not show up in many tables where only the
semi-major axis and flattening are given. The origin is really implicitly defined by the
coordinates assigned to the primary reference point.
In general if a datum covers areas not directly connected by a survey, such as over a large
body of water, there are really different versions of the datum. This is not an academic
point. At least one recent ship grounding in the Caribbean was caused by using the wrong
"NAD 83" in a GPS receiver. They set the GPS receiver to a version of "NAD83" that did
not match the "NAD 83" on the chart.
II.
Why and How Datums Happen
When people first began to map accurately using surveys in an area, they sometimes have
the choice to extend some existing survey point set or beginning anew. When there is no
land connection between the new and old areas, there was no choice until the advent of
satellite surveying they had to begin a new datum. If the old surveys were very far away,
a new datum was almost always begun.
Most countries defined their own map reference system – or their datum. This means that
at political boundaries the maps would not quite line up. Today there are regional (North
American, European) datums as well as global ones. But maps still exist on different
datums, sometimes even for the same area.
Relative Errors Dominate
Datums are realized through a set of physical points and the associated coordinates
(latitude and longitude) for these “marks”. The relative position between a mark and
adjacent or close marks is established using surveying techniques. All accurate surveying
consists of making measurements between points – thus the measurements are relative,
not absolute. (Celestial navigation gives absolute locations, but it is more inaccurate.)
Errors build up as a network of points is extended. The errors are largest where the area is
mountainous. This occurs both because surveying is difficult there, but also because the
mountains cause minor changes in the gravity field of the earth.
3
The surveyor uses gravity to define up, and hence the horizontal. With small changes in
gravity due mountains etc, this causes the survey to diverge from the model ellipsoid of
the earth.
Datums and More Datums
Occasionally when new survey techniques come along the networks are re-surveyed. A
new datum is thus produced. It usually consists of the same physical marks, but new
coordinates. For example there was a major adjustment of the survey data in North
America during the 1920'
s. These efforts lead to the publishing of the North American
Datum of 1927. Satellite surveying and electronic distance measuring equipment pointed
out the distortions in this datum. A new datum based on new measurement was published
– the North American Datum of 1983. These are often called NAD 27 and NAD 83
respectively.
III.
Example of Datum / Datums
A “datum” is defined in various ways, mathematically, for the surveyor, and practically.
It can be thought of as a collection of surveyed points whose locations are accurately
know with respect to each other. Here a hypothetical datum will be discussed to illustrate
some of the common issues.
A set of control points that might be used in the Monterey, CA area are shown below on a
picture.
4
The tide gauge and it'
s ground reference mark are real. Notice that there is a point very
near the tide gauge. This is common to tie the tide measurements to the land
measurements. Here is one of the reference markers for this tide gauge.
Benchmark “Tide” in Monterey CA
It is a bronze disk inserted into a bridge foundation. the name of the agency and the
name/number of the "mark" are also given. (Here the mark shows National Ocean
Survey, Mark 3450M, established in 1983)
The above diagram inside the picture shows the points. The lines connecting the points
are the things actually measured in the survey. The following diagram shows the same
network without the background picture of Monterey.
5
Collections of control points like this are used to define the locations for mapping and are
the user view of a datum. Geodesy books, however, usually begin with the modern
mathematical definition and call this collection a “realization” of the datum.
Multiple Datums – Confusion and Error
However one collection, or datum, may not fit some other set (datum). It is in error with
respect to the second collection of points. This occurs periodically as datums are updated
with new information and survey techniques. It happens about twice a century in the US.
In the last major datum change in the US, points typically “moved” by about 100 m (300
ft).
Mismatched datums are also commonly happen when two sets of control points are
separated by large distances or over an ocean. Accurate use of a map depends on
knowing the datum it is on. On modern topographic maps the datum is often given in the
map legend.
IV.
WGS 84 / NAD 83 - A Standard Datum in Several Names
6
With the advent of satellite navigation systems, it was possible to construct a world wide
datum. These are labeled Geodetic Systems. These were generated by the US Department
of Defense beginning in 1966. They constructed World Geodetic System 1966 (WGS
66), which was not very good. It was followed by WGS 72 which was much better and
then WGS 84. The Soviet Union also constructed a series of these, called SRS'
s with the
last being SRS 90. It should be noted that these WGS'
s include information about the
gravity field as well as an ellipsoid and a realization of the "datum".
WGS 84 is the current standard in the west. The US civilian survey organization, the
National Geodetic Survey (NGS) generated a new datum for North America at the same
time (NAD 83). It is essentially identical to WGS 84.
The world geodesy community has been generating these geodetic reference systems
since the 1990'
s. These are labeled International Terrestrial Reference Systems ( ITRF'
s ).
There have been ITRF 92, ITRY 96, ITRF 96, ITRF 98 etc. As these became refined, the
changes became smaller. They were converging on the real world. In fact, the current
versions include a model of the motion of the crustal plates. This is necessary to preserve
the accuracy. (Monterey California, for example, is on the Pacific Plate and moving north
west at 6 cm per year with respect to the North American Plate only a dozen kilometers
inland).
The US civilian agencies have adopted new a new datum in 2000. The US Department of
Defense has essentially done the same thing, but has kept the name WGS 84. Rather than
change the coordinates of all its know bench marks, it has adjusted the coordinates of the
reference sites used to generate the orbits with the Global Positioning System. Thus the
positions obtained using the over the air ephemeris and no Differential GPS corrections
have changed. GPS counts time in weeks since 1980. The new datums are labeled
WGS 84 (G730) implemented in January 1994 ( GPS Week 730),
WGS 84 (G873) implemented in September 1996, and
WGS 84 (G1150) implemented in October 2002.
These brought WGS into alignment with ITRF 94, ITRF 96 and ITRF 2000 at the few
cm level.
The civilian agencies in the US have been using differential GPS survey techniques to
generate a realization of a new network at better than one part per million (1 ppm or 1 cm
over 10 km). They have achieved an order of magnitude better (0.1 ppm) in most areas.
They have a goal of a High Accuracy Reference Network (HARN) survey marker within
200 km of anyplace in the US.
This contains most of the markers used to define NAD 83, in effect allowing a
redefinition of that datum. A new NAD 2000 is being released. Here is the real primary
control network of the US - the HARN network. This is the realization – how the datum
is really used.
7
The official, high accuracy, coordinates of these points are on file with the US National
Geodetic Survey (NGS). They can be retrieved from the NGS web site.
Note: The vertical networks have typically been separate from the horizontal network.
The NAD 83 was followed by the North American Vertical Datum of 1988 (NAVD 88).
Vertical networks are very closely tied to the gravitational model used in these systems.
V.
Map Legends and Datums
If you examine the legend of a topographic map, it will list the datum use to generate it.
On US Geodetic Survey maps this is in the lower left corner. Here is the corner of the
map covering Monterey, CA. Notice that it says that the map is on NAD 83, but ... look
closely.
8
This is a example of an older map being updated using an overprinting. Many US
topographic maps are the same as the NAD 27 maps with a notation in the legend on how
to adjust the coordinates to NAD 83. There is also often a small cross in the corner
giving the location of the corner coordinates in the new datum.
The different coordinates for the same point in different datums can often be significant.
For example the difference between NAD 27 and NAD 83 can be over 100 meters (300
ft) as it is here. The following shows two small area (7.5 minute series) topographic
maps from central Missouri. One is on the newer NAD83, the other still on NAD27. The
maps have been cut and aligned with by the features. Notice that the coordinates are now
off. The difference is about 20 m in the North/South and 210 m East/West.
9
Map Segments in Two Datums
Showing Latitude Offset
Datum shifts can be very large. In one case, that of the Tokyo Datum and the commonly
used World Geodetic System 1984 (WGS84) the difference is measured in kilometers or
miles.
Because WGS 84 is so important today, a map of the difference between it and common
local datums has been generated. The differences are color coded in bins to make it easier
to use. WGS84 is the default datum for most GPS receivers. Clearly in some areas of the
world, you would be way off using this setting with a locally generated map.
10
VI.
Datums as Rubber Sheets
All older datums have significant distortions. These arise from the accumulation of
survey errors. Over a small area, the difference between two datums is essentially an
offset in north, east, and height. But this offset is not constant over large areas. For
example, the NAD 27 datum has significant systematic distortions. The current standard
for the US is NAD83. This is predominately based on satellite surveys, that are about
two orders of magnitude better than the NAD27 surveys.
The errors in NAD27, when measured by comparing with NAD83 is a slowly varying
function of location. The old NAD27 is like a rubber sheet with weights on it. The best
way to display this distortion is to plot the differences as contour plots.
The latitude shift shows a progression from the northwest at about -20m to the southeast
where it is 40 m. . The difference in the shift is 60 meters. The difference in the
longitude is larger.
11
The latitude difference is about –40 m on the east coast and increased as you move
westward where it reaches 100 m on the west coast. There is a similar difference in the
height, with the range being -15 to –40 m.
Clearly, using one offset for the US, or even one for the eastern US and one for the
western US, leaves significant errors. Using one or two offsets is what most GPS
receivers do when you ask them to display NAD 27 coordinates. The results are not
adequate for navigation.
12